Dynamical Evolution of Barred Galaxies

24 pages, 11 figures, invited review, 2004 DDA meeting in Cannes, april 19-23, Celestial Mechanics & Dynamical Astronomy (in press)Angular momentum redistribution within barred galaxies drives their dynamical evolution. Angular momentum is emitted mainly by near-resonant material in the bar region and absorbed by resonant material mainly in the outer disc and in the halo. This exchange determines the strength of the bar, the decrease of its pattern speed, as well as its morphology. If the galaxy has also a gaseous component and/or a companion or satellite, then these also take part in the angular momentum exchange. During the evolution a bar structure forms in the inner parts of the halo as well. This bar is shorter and fatter than the disc bar and stays so all through the simulation, although its length grows considerably with time. Viewed edge-on, the bar in the disc component acquires a boxy or peanut shape. I describe the families of periodic orbits that explain such structures and review the observations showing that boxy/peanut `bulges\' are in fact just bars seen edge-on